To get maximum power
transfer from the SMPS driver to the TC secondary, the driver output impedance
must be matched to the TC secondary impedance. These are matched when both
impedances are equal. A matched condition also implies that you are then
running your SMPS driver at the max power it can handle - cranked
up to max - and you are putting maximum power into the TC secondary and
streamers.

Of course, the SMPS driver output impedance may be lower than the driven TC
secondary. This would mean that you are running the SMPS at lower/"safer"
power levels, i.e. below the absolute maximum rating. That's generally
considered a good engineering practice (though, for SSTCs, design
for long term reliability can usually be ignored ;-).

When using a ferrite core step-up transformer to
step up the mains voltage and feed this into the secondary base, the
transformer turns ratio between secondary and primary can be used to match the
SMPS and TC secondary impedances: the base impedance of the TC secondary, Z_sec (the
exact value to be measured), will be reflected to the transformer
primary side as an impedance equal to:

Z_sec_reflected = Z_sec * (N_pri/N_sec)^2

and now your remaining task is to match Z_sec_reflected to the SMPS
output impedance. This is easily "matched" by making sure that the
SMPS can handle this low impedance load Z_sec_reflected without blowing up,
i.e. can supply the power P_pri drawn by the primary of the transformer and
delivered to the TC. This power is equal to

P_pri = (V_pri)^2 / Z_sec_reflected
(where V_pri is the voltage applied accross the primary. Assuming 230VAC
mains, it is 350VDC for a full-bridge and 160VDC for a half-bridge)

With this info, you can build the transformer. This isn't as simple as it may
sound, and requires a lot of experimenting. A good introduction and an almost
step-by-step guide for designing your own transformer is available as a TI
tech seminar paper, "Power Transformer Design".

It may be easier to do
this design backwards - first, measure the base impedance of your TC secondary.
Then come up with some realistic output power you'd like. Say, 1000W. In order
for 1000W to be delivered into the secondary base impedance, the step-up
transformer must have an output voltage of

V_sec = SQRT ( Z_sec * P_sec )

This leads to a turns ratio

N_sec/N_pri = V_sec/V_priorN_sec = N_pri * (V_sec/V_pri)(where V_pri is the voltage applied accross
the primary. Assuming 230VAC mains, it is 350VDC for a full-bridge and 160VDC
for a half-bridge)

After you find a ferrite core that can handle the desired 1000 Watts at the TC
resonant frequency, without too high heating losses, you can use the formulas
from the "Power Transformer Design" paper to calculate the minimum
number of primary turns. After that, use the above formula to get the number
of turns required on the secondary winding.

The hopefully clearest way to state all this is that you design the
transformer turns ratio for a given output voltage. The initial base impedance
of the TC secondary is somewhat constant, so that the initial power draw will
be P = U_xfmr_sec^2 / Z_tc_sec.

Because the base impedance can only increase from this value (due to streamer
loading as well as detuning) this power is also the maximum power drawn. With
a specific transformer turns ratio you get out the desired voltage and thus
can set the max power.

The same ideas apply to
the direct TC primary coil drive method. In this
case it is the turns ratio between the air-core primary coil and the TC
secondary, as well as the coupling between these two coils, which will
determine the magnitude of the TC secondary impedance that is seen by the
driver circuit.
When increasing the number of pri turns, the impedance seen at the primary
side increases, approaching the impedance of the secondary, thus reducing
power draw. Decreasing the pri turns count also decreases the impedance seen
by the driver, so power draw increases. Using tighter coupling has a similar
effect like decreasing the pri turns count.

Once again, "impedance matching" isn't anything else than choosing
the pri turns and coupling (well, you want maximum coupling, for sure) in such
a way that the power draw doesn't exceed the maximum power your bridge SMPS (mosfet
and diodes) can handle.

In a sense, this "impedance matching" isn't really one of the
ordinary impedance matchings, because the impedance of the SMPS primary side
is the impedance of the live mains supply, so the output impedance of the
driver is always lower than the "matched" impedance. Then again,
shutting down the mosfets when overcurrent conditions occur does simulates a
higher average output impedance. Also, pulse width modulation, if it is used,
would simulate a higher instantaneous output impedance. But PWM isn't a good
idea for SSTCs...